Just keep the waste on site and then, if a plant is decommissioned, add it to another reactor's pile.
It's not a permanent solution for millions of years, but it's also likely fine for the next 100 years and that's a reasonable tradeoff (imo).
This is just hyperbole though. All the other arguments aside, it's perfectly possible for humans to plan, and make risk estimates, beyond a human life span.
I think a small pile of hot rubbish well hidden is the least of our problems
But I'm not comparing Nuclear to perfection; I'm comparing it to existing alternatives. Climate change is real, the stakes are high, and nuclear brings a lot to the table.
Nuclear can provide base load energy. To provide base load with renewables requires battery storage that doesn't exist. I'm sure the technology exists but whether because expense or other issues, energy grids around the world don't use grid level storage. And consumers are not interested in trading a little reliability for greener grids; they consistently insist that dirty alternatives close the gap.
And very rough estimate here (it is going to vary considerably based on the solar panels and plant in question, but the principle is unchanged): 1 nuclear plant is roughly 4,000 sq km of solar panels. So like 80 Manhattans ever inch of it a solar panel array. The environmental destruction caused by solar panel array and wind farms is real. The amount of mining required to create the materials needed for 4k solar panels also has a very high environmental cost. Nuclear is compact and requires less materials.
We deal with all kinds of waste that we know would be damaging if it was released in the environment. Radioactivity is dangerous, but I would argue far better understood than many other phenomenon (like micro plastics). It is a challenge, but there is no avoiding challenges. The tradeoffs feel well worth it to me.
My point is that we already deal with many substances that are toxic forever. Something about the danger reducing over the course of thousands of years seems to make people more concerned about the future than when the danger is permanent.